Axiomatization of local-global principles for pp-formulas in spaces of orderings

V. Astier; M. Tressl

doi:10.1007/s00153-004-0236-0

Axiomatization of local-global principles for pp-formulas in spaces of orderings

V. Astier, M. Tressl

University College Dublin

Research output: Contribution to journal › Article › peer-review

Abstract

We use a model theoretic approach to investigate properties of local-global principles for positive primitive formulas in spaces of orderings, such as the existence of bounds and the axiomatizability of local-global principles. As a consequence we obtain various classes of special groups satisfying local-global principles for all positive primitive formulas, and we show that local-global principles are preserved by some natural constructions in special groups.

Original language	English
Pages (from-to)	77-95
Number of pages	19
Journal	Archive for Mathematical Logic
Volume	44
Issue number	1
DOIs	https://doi.org/10.1007/s00153-004-0236-0
Publication status	Published - 24 May 2004

Keywords

Isotropy theorem
Local-global principles
Model theory
Positive-primitive formulas
Quadratic forms
Spaces of orderings
Special groups

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10.1007/s00153-004-0236-0

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AB - We use a model theoretic approach to investigate properties of local-global principles for positive primitive formulas in spaces of orderings, such as the existence of bounds and the axiomatizability of local-global principles. As a consequence we obtain various classes of special groups satisfying local-global principles for all positive primitive formulas, and we show that local-global principles are preserved by some natural constructions in special groups.

KW - Isotropy theorem

KW - Local-global principles

KW - Model theory

KW - Positive-primitive formulas

KW - Quadratic forms

KW - Spaces of orderings

KW - Special groups

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DO - 10.1007/s00153-004-0236-0

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VL - 44

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EP - 95

JO - Archive for Mathematical Logic

JF - Archive for Mathematical Logic

SN - 0933-5846

IS - 1

ER -

Axiomatization of local-global principles for pp-formulas in spaces of orderings

Abstract

Keywords

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